{"id":23318,"date":"2021-01-07T21:20:00","date_gmt":"2021-01-08T01:20:00","guid":{"rendered":"https:\/\/www.shortform.com\/blog\/?p=23318"},"modified":"2026-01-22T22:17:59","modified_gmt":"2026-01-23T02:17:59","slug":"hamiltons-rule","status":"publish","type":"post","link":"https:\/\/www.shortform.com\/blog\/hamiltons-rule\/","title":{"rendered":"Hamilton’s Rule: Calculating Kin Altruism"},"content":{"rendered":"\n

What is Hamilton’s Rule? How does Hamilton’s Rule help quantify kin altruism<\/a>?<\/p>\n\n\n\n

Hamilton’s Rule is a mathematical representation of kin altruism. It compares the relatedness and benefit of helping to the cost of doing so.<\/p>\n\n\n\n

Keep reading for more about kin altruism and Hamilton’s Rule.<\/p>\n\n\n\n\n\n\n\n

Kin Altruism and Hamilton’s Rule: Background<\/h2>\n\n\n\n

Now we\u2019ll explore how and why animals show altruistic behaviors, especially toward their family members. Genes don\u2019t just act to protect the individual they\u2019re inside of. We know this because animals frequently help their offspring and relatives, even at risk to themselves. This makes sense if we consider a \u201cselfish gene\u201d to be all<\/em> copies of that gene across the entire population. Then we can assume that individuals will act to protect other individuals who are likely to have the same gene<\/strong>.<\/strong><\/p>\n\n\n\n

Before considering the quantified version of kin altruism, represented by Hamilton’s Rule, we can consider the perceptions and psychology behind these behaviors. The perceived likelihood of relatedness could come from a physical characteristic that the gene gives. For example, if there were a gene for purple hair, you might expect one purple-haired person to act altruistically toward another. However, the odds of a single gene providing both \u201cpurple hair\u201d and \u201caltruism toward purple hair\u201d characteristics are astronomical\u2014remember that genes aren\u2019t conscious, and can\u2019t choose what effects they have on their hosts. Granted, it\u2019s possible that those two genes might tend to be inherited together, as they provide a mutually beneficial environment. <\/p>\n\n\n\n

However, a much easier way for genes to \u201crecognize\u201d themselves in others is through family relations. <\/strong>By definition, close family members will share a lot of the same genes. While it would be very unlikely for a gene to code both for a trait and for altruism toward that same trait, a gene that codes for altruism toward relatives would be successful all on its own. <\/p>\n\n\n\n

Therefore, it should be expected that animals will be altruistic to their family\u2014the more closely related they are, the more altruistic they\u2019ll be. Assuming sexual reproduction, an animal\u2019s offspring will share half of its genes. A sibling will, on average, also share half of the same genes. <\/p>\n\n\n\n

Therefore, from a purely logical standpoint, an animal should consider its child or sibling to be worth half as much as its own life, in terms of preserving genes. That value will go down with more distant relatives. For example, a grandchild will only have 1\/4 of the animal\u2019s genes, so should only be valued at 1\/4 of the creature\u2019s life. You could calculate the \u201crelatedness\u201d of any animal to another by creating a family tree, and counting how many branches you have to move up and down the tree to get from one to the other. <\/p>\n\n\n\n

If g is the number of branches traveled, the relatedness would be (1\/2)<\/strong>g<\/sup><\/strong><\/p>\n\n\n\n

That equation assumes only one common ancestor<\/a>. If there are more, multiply the result by the number of common ancestors in the most recent generation that has them.<\/p>\n\n\n\n

Recognizing Kin<\/strong><\/h3>\n\n\n\n

Naturally, the previous section raises the question of how animals recognize their relatives\u2014or even whether they do. It\u2019s possible that some animals recognize each other simply by appearance, and act altruistically toward animals that resemble them. Others might act altruistically toward any member of their species that happens to be nearby. In that case, we could assume that the odds of any given member of the species being a relative are good enough to make the altruism worth the risk. These behaviors arose due to common situations in nature, and they can misfire\u2014or be made to misfire, like when farmers make nesting hens sit on eggs that aren\u2019t their own.<\/strong><\/p>\n\n\n\n

An interesting evolutionary arms race can be seen between certain species of songbirds and cuckoos who lay eggs in their nests, trying to trigger just such a misfire. Cuckoos try to trick the songbirds into hatching their eggs by laying them in the nest, which takes advantage of the songbirds\u2019 natural altruism toward eggs and small birds in their own nests.<\/p>\n\n\n\n

Those songbirds who recognize the impostors and throw them out will naturally contribute more to the next generation\u2019s gene pool, because they aren\u2019t wasting resources raising cuckoos. Therefore, the next generation will be better at recognizing the cuckoo eggs. On the other hand, those cuckoos whose eggs more closely resemble songbird eggs will have their offspring survive and contribute their <\/em>genes to the next generation. This is a perfect example of selfishness (from the cuckoos) and altruism (from the songbirds) and the struggle between them.<\/p>\n\n\n\n

It\u2019s likely that, in addition to the relatedness value, an animal will also have to consider how certain it is of that relationship.<\/strong> The songbirds from the previous example must be quite certain that the cuckoos are actually their offspring\u2014of course, in that case it turns out that they\u2019re mistaken. <\/strong><\/p>\n\n\n\n

However, it\u2019s usually much easier for most animals to recognize their own offspring than a brother or sister. Therefore, even though a sibling should have the same degree of relation as a child, parent-offspring altruism is much more common than sibling altruism in nature. By that same token, an animal is always 100% certain of its relation to itself, which can often weight decisions in favor of helping itself even over close relatives.<\/p>\n\n\n\n

In reality, there are many considerations other than just relatedness and life vs. death that go into calculating how altruistic to be toward another member of the same species. <\/strong>For example, if an elderly animal can protect a younger relative who has a longer reproductive period still ahead of it, that might shift the decision in favor of altruism. And, naturally, not all acts of altruism result in saving the recipient\u2019s life at the cost of the altruist\u2019s. Risk and reward must be calculated accordingly. This tendency to act altruistically toward your relatives is sometimes called kin selection<\/a><\/em>, though kin altruism <\/em>may be a more accurate term.<\/em><\/p>\n\n\n\n

Of course, animals don\u2019t consciously calculate all of this before acting; it\u2019s done instinctively and almost instantly. It\u2019s similar to a person predicting where a ball will go so that he or she can catch it, even though the math involved in that prediction should be extremely complex. <\/p>\n\n\n\n

Hamilton\u2019s Rule<\/strong><\/h4>\n\n\n\n

There\u2019s a mathematical representation of kin altruism called Hamilton\u2019s Rule.<\/strong> It says that altruism is favored when rB > C<\/em>, (r times B is greater than C) where r is the relatedness <\/em>between the two parties, B is the benefit <\/em>to the recipient, and C is the cost <\/em>to the altruist. <\/p>\n\n\n\n

Because benefit is multiplied by relatedness\u2014which is a fraction, as shown earlier\u2014individuals will weigh benefit proportionally to how closely they\u2019re related<\/strong> <\/em>vs. cost to themselves. If the recipient isn\u2019t related at all, then r = 0 and altruism will never be favored (remember that any number multiplied by zero is zero). Hamilton’s Rule also accounts for such things as an older animal risking its life to save a younger one\u2014in that case, the benefit to the recipient is greater than the cost to the altruist.<\/p>\n","protected":false},"excerpt":{"rendered":"

What is Hamilton’s Rule? How does Hamilton’s Rule help quantify kin altruism? Hamilton’s Rule is a mathematical representation of kin altruism. It compares the relatedness and benefit of helping to the cost of doing so. Keep reading for more about kin altruism and Hamilton’s Rule.<\/p>\n","protected":false},"author":6,"featured_media":7767,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[12,160,24],"tags":[187],"class_list":["post-23318","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-relationships","category-science","category-society","tag-the-selfish-gene","","tg-column-two"],"yoast_head":"\nHamilton's Rule: Calculating Kin Altruism - Shortform Books<\/title>\n<meta name=\"description\" content=\"Animals are more likely to help their relatives, which is known as kin altruism. 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